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Examples of Autoisoptic Curves

  • Boris OdehnalEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)

Abstract

The locus \(k_\alpha \) of all points where two different tangents of a planar curve k meet at a constant angle \(\alpha \) is called the isoptic curve of k. We shall look for curves k that coincide with their isoptic curves \(k_\alpha \) and call them autoisoptic curves. Describing a planar curve k by its support function d allows us to derive a system of two linear ordinary delay differential equations that have to be fulfilled by d in order to make k an autoisoptic curve. Examples of autoisoptic curves different from the only known examples, namely logarithmic spirals, shall be given. We do not provide the most general autoisoptic curves, since these involve ordinary delay differential equations with time dependent delays. We only treat the case of constant delays.

Keywords

Isoptic curve Autoisoptic curve Autoevolutoid Spiraloid Support function Delay differential equation Lambert W function 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of Applied Arts ViennaViennaAustria

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